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PASTRY

PASTRY. Sources. Pastry paper

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PASTRY

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  1. PASTRY

  2. Sources • Pastry paper • “Pastry: Scalable, decentralized object location and routing for large-scale peer-to-peer systems” by Antony Rowstron (Microsoft Research) and Peter Druschel (Rice University), IFIP/ACM International Conference on Distributed Systems Platforms (Middleware), Heidelberg, Germany, pages 329-350, November, 2001 • Pastry Homepage • http://research.microsoft.com/en-us/um/people/antr/Pastry/default.htm

  3. Chord [Sigcomm’01] CAN [Sigcomm’01] Tapestry [TR UCB/CSD-01-1141] PNRP [unpub.] Viceroy [PODC ’02] Kademlia [IPTPS ’02] Small World [Kleinberg ‘99, ‘00] Plaxton Trees [Plaxton et al. ‘97] Generalized Hypercube [Bhuyan et al. ‘84] Related work

  4. Pastry Generic p2p location and routing substrate (DHT) • Self-organizing overlay network (join, departures, locality repair) • Consistent hashing • Lookup/insert object in < log2bN routing steps (expected) • O(log N) per-node state • Network locality heuristics Scalable, fault resilient, self-organizing, locality aware, secure

  5. Pastry: Object distribution 2128 - 1 O Consistent hashing 128 bit circular id space nodeIds(uniform random) objIds/keys (uniform random) Invariant: node with numerically closest nodeId maintains object objId/key nodeIds

  6. Pastry: Object insertion/lookup 2128 - 1 O Msg with key X is routed to live node with nodeId closest to X Problem: complete routing table not feasible X Route(X)

  7. Pastry Node • Represented by 128-bit randomly chosen nodeId (Hash of IP or public key) • NodeId is in base 2b (b is a configuration parameter; b typical value 2 or 4) • Evenly distributed nodeIds along the circular namespace (0-2128 – 1 space). • Routes a message in O(log N) steps to destination • N: size of network • Node state contains: • Leaf Set ( L ) • Routing table ( R ) • Neighborhood Set ( M) CMPT 880: P2P Systems - SFU

  8. Leaf set: L/2 Numerically closest nodes (L is a configuration parameter = 16, 32 typically ) Routing Table (Prefix-based) Neighborhood Set: M physically closest nodes Pastry node state

  9. Pastry node state (Leaf Set) • Serves as a fall back for routing table and contains: • L/2 numerically closest and larger nodeIds • L/2 numerically closest and smaller nodIds • Size of L is typically 2b or 2 x 2b • Nodes in L are numerically close (could be geographically diverse)

  10. Pastry node state: Neighborhood set (M) • Contains the IP addresses and nodeIds of closest nodes according to proximity metric • Size of |M| is typically 2b or 2x2b • Not used in routing, but instead for maintaining locality properties

  11. Node state:Routing Table • Matrix of Log2bN rows and 2b – 1 columns (N is the number of nodes in the network) • Entries in row n match the first n digits of current nodeId AND • Column number follows matched digits: Format: matched digits–column number–rest of ID • Log2b N populated on average

  12. Node10233102 (2), (b = 2, l = 8)

  13. Pastry: Routing Tradeoff • O(log N) routing table size • 2b * log2bN + 2l • O(log N) message forwarding steps

  14. Prefix Routing • Node IDs and keys from randomized namespace (SHA-1) • incremental routing towards destination ID • each node has small set of outgoing routes • log (n) neighbors per node, log (n) hops between any node pair • ID: ABCE • ABC0 • To: ABCE • AB5F • A930

  15. Pastry: Routing table (# 10233102) L nodes in leaf set log2b N Rows (actually log2b 2128= 128/b) 2b columns L neighbors

  16. Pastry: Routing procedure (1) Node is in the leaf set (2) Forward message to a closer node (Better match) (3) Forward towards numerically Closer node (not a better match) D: Message Key Li: ith closest NodeId in leaf set shl(A, B): Length of prefix shared by nodes A and B Rij: (j, i)th entry of routing table

  17. Pastry: Routing procedure If (destination is within range of our leaf set) forward to numerically closest member else letl = length of shared prefix letd= value of l-th digit in D’s address if (Rld exists) forward to Rld else forward to a known node (from ) that (a) shares at least as long a prefix (b) is numerically closer than this node

  18. Pastry: Routing procedure • If message with key D is within range of leaf set, forward to numerically closest leaf • Else forward to node that shares at least one more digit with D in its prefix than current nodeId • If no such node exists, forward to node that shares at least as many digits with D as current nodeId but numerically nearer than current nodeId CMPT 880: P2P Systems - SFU

  19. Pastry: Routing Properties • log2b N steps • O(log N) state d471f1 d467c4 d462ba d46a1c d4213f Look for (d46a1c) d13da3 65a1fc

  20. Pastry: Locality properties Assumption: scalar proximity metric • e.g. ping/RTT delay, # IP hops • traceroute, subnet masks • a node can probe distance to any other node Proximity invariant: Each routing table entry refers to a node close to the local node (in the proximity space), among all nodes with the appropriate nodeId prefix.

  21. d467c4 d471f1 d467c4 Proximity space d462ba d46a1c d4213f Route(d46a1c) d13da3 d4213f 65a1fc 65a1fc d462ba d13da3 Pastry: Geometric Routing in proximity space NodeId space • The proximity distance traveled by message in each routing step is exponentially increasing (entry in row l is chosen from a set of nodes of size N/2bl) • The distance traveled by message from its source increases monotonically at each step (message takes larger and larger strides)

  22. Pastry: Locality properties • Each routing step is local, but there is no guarantee of globally shortest path • Nevertheless, simulations show: • Expected distance traveled by a message in the proximity space is within a small constant of the minimum • Among k nodes with nodeIds closest to the key, message likely to reach the node closest to the source node first

  23. Pastry: Self-organization Initializing and maintaining routing tables and leaf sets • Node addition • Node departure (failure) The goal is to maintain all routing table entries to refer to a near node, among all live nodes with appropriate prefix

  24. Pastry: Node addition • New node X contacts nearby node A • A routes “join” message to X, which arrives to Z, closest to X • X obtains leaf set from Z, i’th row for routing table from i’th node from A to Z • X informs any nodes that need to be aware of its arrival • X also improves its table locality by requesting neighborhood sets from all nodes X knows • In practice: optimistic approach

  25. Pastry: Node addition d471f1 Z=d467c4 d462ba X=d46a1c d4213f New node: X=d46a1c A is X’s neighbor Route(d46a1c) d13da3 A = 65a1fc

  26. d471f1 d467c4 d467c4 d462ba d46a1c d4213f Proximity space Route(d46a1c) d13da3 65a1fc New node: d46a1c NodeId space d4213f 65a1fc d462ba d13da3 Pastry: Node addition B1 is first row of B X X is close to A, B is close to B1. Why X is close to B1? The expected distance from B to its row one entries (B1) is much larger than the expected distance from A to B (chosen from exponentially decreasing set size)

  27. Node departure (failure) • Leaf set repair (eager – all the time): • Leaf set members exchange keep-alive messages • request set from furthest live node in set • Routing table repair (lazy – upon failure): • get table from peers in the same row, if not found – from higher rows • Neighborhood set repair (eager)

  28. Pastry: Summary • Generic p2p overlay network • Scalable, fault resilient, self-organizing, secure • O(log N) routing steps (expected) • O(log N) routing table size • Network locality properties

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